Wilbert Zweistein's Objection to Equivalence Principle

In summary, the equivalence principle might or might not extend to all theories of quantum gravity, it is difficult to distinguish the Unruh effect from Hawking radiation, and a possible physical origin for the heating effect in the case of hovering (by means of rockets, say) outside a star could be ascribed if we assume the quantum field is in the vacuum state according to inertial observers.
  • #1
ergospherical
1,045
1,335
I'd like to share the following competition problem:

1651672013471.png


My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.
 
  • Like
Likes atyy
Physics news on Phys.org
  • #2
Possibly, but I don’t think that the Unruh effect is local and I would also think that it would be very difficult to distinguish it from Hawking radiation.
 
  • Like
Likes VVS2000, Demystifier and vanhees71
  • #3
Does the equivalence principle extend to all theories of quantum gravity?
 
  • Like
Likes vanhees71
  • #4
Dale said:
Possibly, but I don’t think that the Unruh effect is local and I would also think that it would be very difficult to distinguish it from Hawking radiation.
But something like a star or a planet doesn’t emit Hawking radiation, right?
 
  • Like
Likes vanhees71
  • #5
ergospherical said:
My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.
The Unruh effect is due to proper acceleration, and would be there, in principle, whether the lab was accelerating in free space or was sitting at rest in the gravitational field of a large mass. So it could not be used to distinguish those two cases.

OTOH, if by "gravitational attraction" the question means coordinate acceleration towards a large mass, the lab would be in free fall in this case, and although there would indeed be no Unruh effect in this case, there would also be a reading of zero on the lab's accelerometer (which could be as simple as a bathroom scale), which would be a much easier and more straightforward way of distinguishing the two cases.
 
  • Like
  • Informative
Likes Orodruin, geshel, vanhees71 and 2 others
  • #6
Oh, I didn’t know that. Can we ascribe a physical origin to the heating effect in the case of hovering (by means of rockets, say) outside a star?
 
  • #7
ergospherical said:
Can we ascribe a physical origin to the heating effect in the case of hovering (by means of rockets, say) outside a star?
I should actually rephrase my previous statement. The Unruh effect is derived assuming flat spacetime and the quantum field being in the vacuum state according to inertial observers. (See below for why the qualifier "according to inertial observers" is necessary.) If a gravitating mass is present, spacetime is neither flat nor in the vacuum state according to inertial observers, so it's not clear whether the Unruh effect would even be predicted in this case. If we assume it would be predicted in the "hovering in the vacuum region above a gravitating mass" case based on something like the equivalence principle, then its physical origin would be what I describe below.

The qualifier I gave above about the vacuum state is necessary because the reason the Unruh effect is predicted at all is that which state of the quantum field is the "vacuum" is different for inertial observers and accelerated observers. More precisely, the concept of "vacuum state" for the quantum field requires a concept of "time translations" for its definition, and inertial observers and accelerated observers have different concepts of "time translations" (roughly speaking, because the inertial Killing vector field and the boost Killing vector field in Minkowski spacetime are different). The derivation of the Unruh effect amounts to showing that the state of the quantum field that is a vacuum state in flat spacetime for inertial observers is not a vacuum state for accelerated observers; instead, it turns out to look like a thermal state at the Unruh radiation temperature.

The reference from which I first learned all this is Wald's monograph, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Unfortunately I have never found it online and I don't know of a good online discussion of the above, although there probably is one.
 
  • Like
Likes vanhees71 and ergospherical
  • #8
Fascinating stuff. I’ll look for the book later this week (I recall it being referenced in H. Reall’s lecture notes); that’s probably more efficient than asking a bunch of groundwork questions here.
 
  • #9
ergospherical said:
I’ll look for the book later this week
It's on Amazon:

https://www.amazon.com/dp/0226870278/?tag=pfamazon01-20

When I said I have never found it online, I meant I have never found a digital version of it, or, for example, a preprint on arxiv.org or some other similar freely available online source that covers the same material.
 
  • Like
Likes vanhees71 and ergospherical
  • #10
Thanks, I can go borrow it but the next couple of days are slightly nuts so probably won’t stop by the lib until the weekend. :)
 
  • #11
ergospherical said:
Thanks, I can go borrow it but the next couple of days are slightly nuts so probably won’t stop by the lib until the weekend. :)
If you can get through the book in a weekend you are definitely quicker at it than I am. :wink:
 
  • Like
Likes vanhees71
  • #12
One thing or watch for in discussions of the equivalence principle is that it is local in time as well as space. Ohanian, for example, has published a number of alleged refutations of the principle that other physicists reject because they ignore the time element.
 
  • Like
Likes Orodruin, vanhees71 and PeterDonis
  • #13
PeroK said:
Does the equivalence principle extend to all theories of quantum gravity?
Does it extend to any theory of quantum gravity?
 
  • Like
Likes vanhees71 and PeroK
  • #14
Good question. I'd say it the other way: A good theory of the gravitational interaction should obey (at least the weak) equivalence principle since it's empirically so well established.

As demonstrated by this discussion the problem with the equivalence principle or rather the equivalence principles is that it is usually discussed in the heuristic introductions to GR and then not further qualified given the fully exposed theory (a fate it shares with the discussions of the Michelson Morley experiment, which is usually also only discussed as a "crucial experiment" for the heuristical motivation of SR).

A clear way to state the principle is that the GR spacetime model is a Pseudo-Riemannian manifold with the fundamental form of the signature (1,3) or, equivalently (3,1). Physically that means that the notion of inertial frames is local an that at any point in spacetime there's always a local inertial frame of reference. That's of course not a good way to heuristically motivate GR but it should be the final clarifying statement about the content of the (then even strong!) equivalence principle.

For particle physicists another convincing semi-heuristic argument is that relativistic models of the gravitational interaction can be built by "gauging" Poincare invariance, which becomes then a local symmetry and thus you have a gauge theory with the general diffeomorphism invariance as the gauge group, which usually is called "general covariance". Together with the fact that there are particles with spin that leads to the statement that GR spacetime is described as a Einstein-Cartan manifold with torsion. In the usual "macroscopic" phenomenology, where gravitation plays a practical role, all you have is classical matter ("continuum mechanics") and the em. field as sources, and there the theory specializes to usual GR. If there is torsion, it's inside "polarized matter" and thus pretty difficult to observe.
 

FAQ: Wilbert Zweistein's Objection to Equivalence Principle

1. What is Wilbert Zweistein's Objection to Equivalence Principle?

Wilbert Zweistein's Objection to Equivalence Principle is a thought experiment proposed by physicist Wilbert Zweistein to challenge the validity of the Equivalence Principle in Einstein's Theory of General Relativity.

2. What is the Equivalence Principle?

The Equivalence Principle states that the effects of gravity and acceleration are equivalent. This means that an observer in a uniformly accelerating frame of reference would experience the same effects as an observer in a gravitational field.

3. What is the significance of Wilbert Zweistein's objection?

Wilbert Zweistein's objection raises doubts about the validity of the Equivalence Principle and its role in Einstein's Theory of General Relativity. It challenges our understanding of gravity and the nature of space-time.

4. How does Wilbert Zweistein's thought experiment work?

In the thought experiment, Zweistein imagines a box filled with gas that is accelerating upward in a gravitational field. He then introduces a small hole in the box and observes the behavior of the gas particles. According to the Equivalence Principle, the gas particles should behave as if they are in a uniform gravitational field, but Zweistein argues that this is not the case.

5. What are the implications of Wilbert Zweistein's objection?

If Zweistein's objection is valid, it would mean that the Equivalence Principle is not a fundamental law of nature and would require a re-evaluation of our understanding of gravity and space-time. It could also potentially lead to a new theory of gravity that can better explain the observed phenomena.

Similar threads

Replies
44
Views
5K
Replies
36
Views
3K
Replies
32
Views
3K
Replies
10
Views
808
Replies
24
Views
2K
Replies
38
Views
4K
Back
Top